Difference between revisions of "1958 AHSME Problems/Problem 40"
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== Solution == | == Solution == | ||
− | <math> | + | Using the recursive definition, we find that <math>a_3=33</math>. |
+ | |||
+ | ==Sidenote== | ||
+ | All the terms in the sequence <math>a_n</math> are integers. In fact, the sequence <math>a_n</math> satisfies the recursion <math>a_n=3a_{n-1}+a_{n-2}</math> (Prove it!). | ||
== See Also == | == See Also == |
Latest revision as of 23:44, 8 March 2024
Contents
Problem
Given ,
, and the general relation
for
. Then
equals:
Solution
Using the recursive definition, we find that .
Sidenote
All the terms in the sequence are integers. In fact, the sequence
satisfies the recursion
(Prove it!).
See Also
1958 AHSC (Problems • Answer Key • Resources) | ||
Preceded by Problem 39 |
Followed by Problem 41 | |
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All AHSME Problems and Solutions |
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